Increasing demand for real-time applications such as teleoperation, remote control of a process, and live video streaming has led to the need for more efficient and reliable transport protocols that can satisfy strict latency requirements. Emerging multipath communication can help to achieve such goals. However, existing multipath protocols, such as Multipath TCP and Multipath QUIC fall short on real-time applications, as they rely on retransmissions and congestion control, leading to higher latencies on lossy links. This paper proposes DMTP, a new deadline-aware multipath transport protocol based on the SCION Internet architecture to support real-time applications with strict latency requirements. Our evaluations show that DMTP outperforms Multipath TCP and Multipath QUIC over lossy links by more than 40% in terms of the number of packets transferred within their deadline when the loss rate is above 2%.